Blanchard, Romain et Carassus, Laurence, Multiple-priors optimal investment in discrete time for unbounded utility function, Annals of applied probability , 28(3), 2018, pp. 1856-1892
This paper investigates the problem of maximizing expected terminal utility in a discrete-time financial market model with a finite horizon under nondominated model uncertainty. We use a dynamic programming framework together with measurable selection arguments to prove that under mild integrability conditions, an optimal portfolio exists for an unbounded utility function defined on the half-real line.